
/*
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 */
#include "slu_sdefs.h"

void
sgssvx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
       int *etree, char *equed, float *R, float *C,
       SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
       SuperMatrix *B, SuperMatrix *X, float *recip_pivot_growth,
       float *rcond, float *ferr, float *berr,
       mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info )
{
    /*
     * Purpose
     * =======
     *
     * SGSSVX solves the system of linear equations A*X=B or A'*X=B, using
     * the LU factorization from sgstrf(). Error bounds on the solution and
     * a condition estimate are also provided. It performs the following steps:
     *
     *   1. If A is stored column-wise (A->Stype = SLU_NC):
     *
     *      1.1. If options->Equil = YES, scaling factors are computed to
     *           equilibrate the system:
     *           options->Trans = NOTRANS:
     *               diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
     *           options->Trans = TRANS:
     *               (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
     *           options->Trans = CONJ:
     *               (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
     *           Whether or not the system will be equilibrated depends on the
     *           scaling of the matrix A, but if equilibration is used, A is
     *           overwritten by diag(R)*A*diag(C) and B by diag(R)*B
     *           (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans
     *           = TRANS or CONJ).
     *
     *      1.2. Permute columns of A, forming A*Pc, where Pc is a permutation
     *           matrix that usually preserves sparsity.
     *           For more details of this step, see sp_preorder.c.
     *
     *      1.3. If options->Fact != FACTORED, the LU decomposition is used to
     *           factor the matrix A (after equilibration if options->Equil = YES)
     *           as Pr*A*Pc = L*U, with Pr determined by partial pivoting.
     *
     *      1.4. Compute the reciprocal pivot growth factor.
     *
     *      1.5. If some U(i,i) = 0, so that U is exactly singular, then the
     *           routine returns with info = i. Otherwise, the factored form of
     *           A is used to estimate the condition number of the matrix A. If
     *           the reciprocal of the condition number is less than machine
     *           precision, info = A->ncol+1 is returned as a warning, but the
     *           routine still goes on to solve for X and computes error bounds
     *           as described below.
     *
     *      1.6. The system of equations is solved for X using the factored form
     *           of A.
     *
     *      1.7. If options->IterRefine != NOREFINE, iterative refinement is
     *           applied to improve the computed solution matrix and calculate
     *           error bounds and backward error estimates for it.
     *
     *      1.8. If equilibration was used, the matrix X is premultiplied by
     *           diag(C) (if options->Trans = NOTRANS) or diag(R)
     *           (if options->Trans = TRANS or CONJ) so that it solves the
     *           original system before equilibration.
     *
     *   2. If A is stored row-wise (A->Stype = SLU_NR), apply the above algorithm
     *      to the transpose of A:
     *
     *      2.1. If options->Equil = YES, scaling factors are computed to
     *           equilibrate the system:
     *           options->Trans = NOTRANS:
     *               diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B
     *           options->Trans = TRANS:
     *               (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B
     *           options->Trans = CONJ:
     *               (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B
     *           Whether or not the system will be equilibrated depends on the
     *           scaling of the matrix A, but if equilibration is used, A' is
     *           overwritten by diag(R)*A'*diag(C) and B by diag(R)*B
     *           (if trans='N') or diag(C)*B (if trans = 'T' or 'C').
     *
     *      2.2. Permute columns of transpose(A) (rows of A),
     *           forming transpose(A)*Pc, where Pc is a permutation matrix that
     *           usually preserves sparsity.
     *           For more details of this step, see sp_preorder.c.
     *
     *      2.3. If options->Fact != FACTORED, the LU decomposition is used to
     *           factor the transpose(A) (after equilibration if
     *           options->Fact = YES) as Pr*transpose(A)*Pc = L*U with the
     *           permutation Pr determined by partial pivoting.
     *
     *      2.4. Compute the reciprocal pivot growth factor.
     *
     *      2.5. If some U(i,i) = 0, so that U is exactly singular, then the
     *           routine returns with info = i. Otherwise, the factored form
     *           of transpose(A) is used to estimate the condition number of the
     *           matrix A. If the reciprocal of the condition number
     *           is less than machine precision, info = A->nrow+1 is returned as
     *           a warning, but the routine still goes on to solve for X and
     *           computes error bounds as described below.
     *
     *      2.6. The system of equations is solved for X using the factored form
     *           of transpose(A).
     *
     *      2.7. If options->IterRefine != NOREFINE, iterative refinement is
     *           applied to improve the computed solution matrix and calculate
     *           error bounds and backward error estimates for it.
     *
     *      2.8. If equilibration was used, the matrix X is premultiplied by
     *           diag(C) (if options->Trans = NOTRANS) or diag(R)
     *           (if options->Trans = TRANS or CONJ) so that it solves the
     *           original system before equilibration.
     *
     *   See supermatrix.h for the definition of 'SuperMatrix' structure.
     *
     * Arguments
     * =========
     *
     * options (input) superlu_options_t*
     *         The structure defines the input parameters to control
     *         how the LU decomposition will be performed and how the
     *         system will be solved.
     *
     * A       (input/output) SuperMatrix*
     *         Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
     *         of the linear equations is A->nrow. Currently, the type of A can be:
     *         Stype = SLU_NC or SLU_NR, Dtype = SLU_D, Mtype = SLU_GE.
     *         In the future, more general A may be handled.
     *
     *         On entry, If options->Fact = FACTORED and equed is not 'N',
     *         then A must have been equilibrated by the scaling factors in
     *         R and/or C.
     *         On exit, A is not modified if options->Equil = NO, or if
     *         options->Equil = YES but equed = 'N' on exit.
     *         Otherwise, if options->Equil = YES and equed is not 'N',
     *         A is scaled as follows:
     *         If A->Stype = SLU_NC:
     *           equed = 'R':  A := diag(R) * A
     *           equed = 'C':  A := A * diag(C)
     *           equed = 'B':  A := diag(R) * A * diag(C).
     *         If A->Stype = SLU_NR:
     *           equed = 'R':  transpose(A) := diag(R) * transpose(A)
     *           equed = 'C':  transpose(A) := transpose(A) * diag(C)
     *           equed = 'B':  transpose(A) := diag(R) * transpose(A) * diag(C).
     *
     * perm_c  (input/output) int*
     *	   If A->Stype = SLU_NC, Column permutation vector of size A->ncol,
     *         which defines the permutation matrix Pc; perm_c[i] = j means
     *         column i of A is in position j in A*Pc.
     *         On exit, perm_c may be overwritten by the product of the input
     *         perm_c and a permutation that postorders the elimination tree
     *         of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
     *         is already in postorder.
     *
     *         If A->Stype = SLU_NR, column permutation vector of size A->nrow,
     *         which describes permutation of columns of transpose(A)
     *         (rows of A) as described above.
     *
     * perm_r  (input/output) int*
     *         If A->Stype = SLU_NC, row permutation vector of size A->nrow,
     *         which defines the permutation matrix Pr, and is determined
     *         by partial pivoting.  perm_r[i] = j means row i of A is in
     *         position j in Pr*A.
     *
     *         If A->Stype = SLU_NR, permutation vector of size A->ncol, which
     *         determines permutation of rows of transpose(A)
     *         (columns of A) as described above.
     *
     *         If options->Fact = SamePattern_SameRowPerm, the pivoting routine
     *         will try to use the input perm_r, unless a certain threshold
     *         criterion is violated. In that case, perm_r is overwritten by a
     *         new permutation determined by partial pivoting or diagonal
     *         threshold pivoting.
     *         Otherwise, perm_r is output argument.
     *
     * etree   (input/output) int*,  dimension (A->ncol)
     *         Elimination tree of Pc'*A'*A*Pc.
     *         If options->Fact != FACTORED and options->Fact != DOFACT,
     *         etree is an input argument, otherwise it is an output argument.
     *         Note: etree is a vector of parent pointers for a forest whose
     *         vertices are the integers 0 to A->ncol-1; etree[root]==A->ncol.
     *
     * equed   (input/output) char*
     *         Specifies the form of equilibration that was done.
     *         = 'N': No equilibration.
     *         = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
     *         = 'C': Column equilibration, i.e., A was postmultiplied by diag(C).
     *         = 'B': Both row and column equilibration, i.e., A was replaced
     *                by diag(R)*A*diag(C).
     *         If options->Fact = FACTORED, equed is an input argument,
     *         otherwise it is an output argument.
     *
     * R       (input/output) float*, dimension (A->nrow)
     *         The row scale factors for A or transpose(A).
     *         If equed = 'R' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
     *             (if A->Stype = SLU_NR) is multiplied on the left by diag(R).
     *         If equed = 'N' or 'C', R is not accessed.
     *         If options->Fact = FACTORED, R is an input argument,
     *             otherwise, R is output.
     *         If options->zFact = FACTORED and equed = 'R' or 'B', each element
     *             of R must be positive.
     *
     * C       (input/output) float*, dimension (A->ncol)
     *         The column scale factors for A or transpose(A).
     *         If equed = 'C' or 'B', A (if A->Stype = SLU_NC) or transpose(A)
     *             (if A->Stype = SLU_NR) is multiplied on the right by diag(C).
     *         If equed = 'N' or 'R', C is not accessed.
     *         If options->Fact = FACTORED, C is an input argument,
     *             otherwise, C is output.
     *         If options->Fact = FACTORED and equed = 'C' or 'B', each element
     *             of C must be positive.
     *
     * L       (output) SuperMatrix*
     *	   The factor L from the factorization
     *             Pr*A*Pc=L*U              (if A->Stype SLU_= NC) or
     *             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
     *         Uses compressed row subscripts storage for supernodes, i.e.,
     *         L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
     *
     * U       (output) SuperMatrix*
     *	   The factor U from the factorization
     *             Pr*A*Pc=L*U              (if A->Stype = SLU_NC) or
     *             Pr*transpose(A)*Pc=L*U   (if A->Stype = SLU_NR).
     *         Uses column-wise storage scheme, i.e., U has types:
     *         Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
     *
     * work    (workspace/output) void*, size (lwork) (in bytes)
     *         User supplied workspace, should be large enough
     *         to hold data structures for factors L and U.
     *         On exit, if fact is not 'F', L and U point to this array.
     *
     * lwork   (input) int
     *         Specifies the size of work array in bytes.
     *         = 0:  allocate space internally by system malloc;
     *         > 0:  use user-supplied work array of length lwork in bytes,
     *               returns error if space runs out.
     *         = -1: the routine guesses the amount of space needed without
     *               performing the factorization, and returns it in
     *               mem_usage->total_needed; no other side effects.
     *
     *         See argument 'mem_usage' for memory usage statistics.
     *
     * B       (input/output) SuperMatrix*
     *         B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
     *         On entry, the right hand side matrix.
     *         If B->ncol = 0, only LU decomposition is performed, the triangular
     *                         solve is skipped.
     *         On exit,
     *            if equed = 'N', B is not modified; otherwise
     *            if A->Stype = SLU_NC:
     *               if options->Trans = NOTRANS and equed = 'R' or 'B',
     *                  B is overwritten by diag(R)*B;
     *               if options->Trans = TRANS or CONJ and equed = 'C' of 'B',
     *                  B is overwritten by diag(C)*B;
     *            if A->Stype = SLU_NR:
     *               if options->Trans = NOTRANS and equed = 'C' or 'B',
     *                  B is overwritten by diag(C)*B;
     *               if options->Trans = TRANS or CONJ and equed = 'R' of 'B',
     *                  B is overwritten by diag(R)*B.
     *
     * X       (output) SuperMatrix*
     *         X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
     *         If info = 0 or info = A->ncol+1, X contains the solution matrix
     *         to the original system of equations. Note that A and B are modified
     *         on exit if equed is not 'N', and the solution to the equilibrated
     *         system is inv(diag(C))*X if options->Trans = NOTRANS and
     *         equed = 'C' or 'B', or inv(diag(R))*X if options->Trans = 'T' or 'C'
     *         and equed = 'R' or 'B'.
     *
     * recip_pivot_growth (output) float*
     *         The reciprocal pivot growth factor max_j( norm(A_j)/norm(U_j) ).
     *         The infinity norm is used. If recip_pivot_growth is much less
     *         than 1, the stability of the LU factorization could be poor.
     *
     * rcond   (output) float*
     *         The estimate of the reciprocal condition number of the matrix A
     *         after equilibration (if done). If rcond is less than the machine
     *         precision (in particular, if rcond = 0), the matrix is singular
     *         to working precision. This condition is indicated by a return
     *         code of info > 0.
     *
     * FERR    (output) float*, dimension (B->ncol)
     *         The estimated forward error bound for each solution vector
     *         X(j) (the j-th column of the solution matrix X).
     *         If XTRUE is the true solution corresponding to X(j), FERR(j)
     *         is an estimated upper bound for the magnitude of the largest
     *         element in (X(j) - XTRUE) divided by the magnitude of the
     *         largest element in X(j).  The estimate is as reliable as
     *         the estimate for RCOND, and is almost always a slight
     *         overestimate of the true error.
     *         If options->IterRefine = NOREFINE, ferr = 1.0.
     *
     * BERR    (output) float*, dimension (B->ncol)
     *         The componentwise relative backward error of each solution
     *         vector X(j) (i.e., the smallest relative change in
     *         any element of A or B that makes X(j) an exact solution).
     *         If options->IterRefine = NOREFINE, berr = 1.0.
     *
     * mem_usage (output) mem_usage_t*
     *         Record the memory usage statistics, consisting of following fields:
     *         - for_lu (float)
     *           The amount of space used in bytes for L\U data structures.
     *         - total_needed (float)
     *           The amount of space needed in bytes to perform factorization.
     *         - expansions (int)
     *           The number of memory expansions during the LU factorization.
     *
     * stat   (output) SuperLUStat_t*
     *        Record the statistics on runtime and floating-point operation count.
     *        See util.h for the definition of 'SuperLUStat_t'.
     *
     * info    (output) int*
     *         = 0: successful exit
     *         < 0: if info = -i, the i-th argument had an illegal value
     *         > 0: if info = i, and i is
     *              <= A->ncol: U(i,i) is exactly zero. The factorization has
     *                    been completed, but the factor U is exactly
     *                    singular, so the solution and error bounds
     *                    could not be computed.
     *              = A->ncol+1: U is nonsingular, but RCOND is less than machine
     *                    precision, meaning that the matrix is singular to
     *                    working precision. Nevertheless, the solution and
     *                    error bounds are computed because there are a number
     *                    of situations where the computed solution can be more
     *                    accurate than the value of RCOND would suggest.
     *              > A->ncol+1: number of bytes allocated when memory allocation
     *                    failure occurred, plus A->ncol.
     *
     */

    DNformat  *Bstore, *Xstore;
    float    *Bmat, *Xmat;
    int       ldb, ldx, nrhs;
    SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
    SuperMatrix AC; /* Matrix postmultiplied by Pc */
    int       colequ, equil, nofact, notran, rowequ, permc_spec;
    trans_t   trant;
    char      norm[1];
    int       i, j, info1;
    float    amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
    int       relax, panel_size;
    float    diag_pivot_thresh, drop_tol;
    double    t0;      /* temporary time */
    double    *utime;

    /* External functions */
    extern float slangs(char *, SuperMatrix *);
    extern double slamch_(char *);

    Bstore = B->Store;
    Xstore = X->Store;
    Bmat   = Bstore->nzval;
    Xmat   = Xstore->nzval;
    ldb    = Bstore->lda;
    ldx    = Xstore->lda;
    nrhs   = B->ncol;

    *info = 0;
    nofact = (options->Fact != FACTORED);
    equil = (options->Equil == YES);
    notran = (options->Trans == NOTRANS);
    if ( nofact ) {
        *(unsigned char *)equed = 'N';
        rowequ = FALSE;
        colequ = FALSE;
    } else {
        rowequ = lsame_(equed, "R") || lsame_(equed, "B");
        colequ = lsame_(equed, "C") || lsame_(equed, "B");
        smlnum = slamch_("Safe minimum");
        bignum = 1. / smlnum;
    }

#if 0
    printf("dgssvx: Fact=%4d, Trans=%4d, equed=%c\n",
           options->Fact, options->Trans, *equed);
#endif

    /* Test the input parameters */
    if (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
            options->Fact != SamePattern_SameRowPerm &&
            !notran && options->Trans != TRANS && options->Trans != CONJ &&
            !equil && options->Equil != NO)
        *info = -1;
    else if ( A->nrow != A->ncol || A->nrow < 0 ||
              (A->Stype != SLU_NC && A->Stype != SLU_NR) ||
              A->Dtype != SLU_S || A->Mtype != SLU_GE )
        *info = -2;
    else if (options->Fact == FACTORED &&
             !(rowequ || colequ || lsame_(equed, "N")))
        *info = -6;
    else {
        if (rowequ) {
            rcmin = bignum;
            rcmax = 0.;
            for (j = 0; j < A->nrow; ++j) {
                rcmin = SUPERLU_MIN(rcmin, R[j]);
                rcmax = SUPERLU_MAX(rcmax, R[j]);
            }
            if (rcmin <= 0.) *info = -7;
            else if ( A->nrow > 0)
                rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
            else rowcnd = 1.;
        }
        if (colequ && *info == 0) {
            rcmin = bignum;
            rcmax = 0.;
            for (j = 0; j < A->nrow; ++j) {
                rcmin = SUPERLU_MIN(rcmin, C[j]);
                rcmax = SUPERLU_MAX(rcmax, C[j]);
            }
            if (rcmin <= 0.) *info = -8;
            else if (A->nrow > 0)
                colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
            else colcnd = 1.;
        }
        if (*info == 0) {
            if ( lwork < -1 ) *info = -12;
            else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
                      B->Stype != SLU_DN || B->Dtype != SLU_S ||
                      B->Mtype != SLU_GE )
                *info = -13;
            else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
                      (B->ncol != 0 && B->ncol != X->ncol) ||
                      X->Stype != SLU_DN ||
                      X->Dtype != SLU_S || X->Mtype != SLU_GE )
                *info = -14;
        }
    }
    if (*info != 0) {
        i = -(*info);
        xerbla_("sgssvx", &i);
        return;
    }

    /* Initialization for factor parameters */
    panel_size = sp_ienv(1);
    relax      = sp_ienv(2);
    diag_pivot_thresh = options->DiagPivotThresh;
    drop_tol   = 0.0;

    utime = stat->utime;

    /* Convert A to SLU_NC format when necessary. */
    if ( A->Stype == SLU_NR ) {
        NRformat *Astore = A->Store;
        AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
        sCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
                               Astore->nzval, Astore->colind, Astore->rowptr,
                               SLU_NC, A->Dtype, A->Mtype);
        if ( notran ) { /* Reverse the transpose argument. */
            trant = TRANS;
            notran = 0;
        } else {
            trant = NOTRANS;
            notran = 1;
        }
    } else { /* A->Stype == SLU_NC */
        trant = options->Trans;
        AA = A;
    }

    if ( nofact && equil ) {
        t0 = SuperLU_timer_();
        /* Compute row and column scalings to equilibrate the matrix A. */
        sgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);

        if ( info1 == 0 ) {
            /* Equilibrate matrix A. */
            slaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
            rowequ = lsame_(equed, "R") || lsame_(equed, "B");
            colequ = lsame_(equed, "C") || lsame_(equed, "B");
        }
        utime[EQUIL] = SuperLU_timer_() - t0;
    }

    if ( nrhs > 0 ) {
        /* Scale the right hand side if equilibration was performed. */
        if ( notran ) {
            if ( rowequ ) {
                for (j = 0; j < nrhs; ++j)
                    for (i = 0; i < A->nrow; ++i) {
                        Bmat[i + j*ldb] *= R[i];
                    }
            }
        } else if ( colequ ) {
            for (j = 0; j < nrhs; ++j)
                for (i = 0; i < A->nrow; ++i) {
                    Bmat[i + j*ldb] *= C[i];
                }
        }
    }

    if ( nofact ) {

        t0 = SuperLU_timer_();
        /*
         * Gnet column permutation vector perm_c[], according to permc_spec:
         *   permc_spec = NATURAL:  natural ordering
         *   permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
         *   permc_spec = MMD_ATA:  minimum degree on structure of A'*A
         *   permc_spec = COLAMD:   approximate minimum degree column ordering
         *   permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
         */
        permc_spec = options->ColPerm;
        if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
            get_perm_c(permc_spec, AA, perm_c);
        utime[COLPERM] = SuperLU_timer_() - t0;

        t0 = SuperLU_timer_();
        sp_preorder(options, AA, perm_c, etree, &AC);
        utime[ETREE] = SuperLU_timer_() - t0;

        /*	printf("Factor PA = LU ... relax %d\tw %d\tmaxsuper %d\trowblk %d\n",
        	       relax, panel_size, sp_ienv(3), sp_ienv(4));
        	fflush(stdout); */

        /* Compute the LU factorization of A*Pc. */
        t0 = SuperLU_timer_();
        sgstrf(options, &AC, drop_tol, relax, panel_size,
               etree, work, lwork, perm_c, perm_r, L, U, stat, info);
        utime[FACT] = SuperLU_timer_() - t0;

        if ( lwork == -1 ) {
            mem_usage->total_needed = *info - A->ncol;
            return;
        }
    }

    if ( options->PivotGrowth ) {
        if ( *info > 0 ) {
            if ( *info <= A->ncol ) {
                /* Compute the reciprocal pivot growth factor of the leading
                   rank-deficient *info columns of A. */
                *recip_pivot_growth = sPivotGrowth(*info, AA, perm_c, L, U);
            }
            return;
        }

        /* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
        *recip_pivot_growth = sPivotGrowth(A->ncol, AA, perm_c, L, U);
    }

    if ( options->ConditionNumber ) {
        /* Estimate the reciprocal of the condition number of A. */
        t0 = SuperLU_timer_();
        if ( notran ) {
            *(unsigned char *)norm = '1';
        } else {
            *(unsigned char *)norm = 'I';
        }
        anorm = slangs(norm, AA);
        sgscon(norm, L, U, anorm, rcond, stat, info);
        utime[RCOND] = SuperLU_timer_() - t0;
    }

    if ( nrhs > 0 ) {
        /* Compute the solution matrix X. */
        for (j = 0; j < nrhs; j++)  /* Save a copy of the right hand sides */
            for (i = 0; i < B->nrow; i++)
                Xmat[i + j*ldx] = Bmat[i + j*ldb];

        t0 = SuperLU_timer_();
        sgstrs (trant, L, U, perm_c, perm_r, X, stat, info);
        utime[SOLVE] = SuperLU_timer_() - t0;

        /* Use iterative refinement to improve the computed solution and compute
           error bounds and backward error estimates for it. */
        t0 = SuperLU_timer_();
        if ( options->IterRefine != NOREFINE ) {
            sgsrfs(trant, AA, L, U, perm_c, perm_r, equed, R, C, B,
                   X, ferr, berr, stat, info);
        } else {
            for (j = 0; j < nrhs; ++j) ferr[j] = berr[j] = 1.0;
        }
        utime[REFINE] = SuperLU_timer_() - t0;

        /* Transform the solution matrix X to a solution of the original system. */
        if ( notran ) {
            if ( colequ ) {
                for (j = 0; j < nrhs; ++j)
                    for (i = 0; i < A->nrow; ++i) {
                        Xmat[i + j*ldx] *= C[i];
                    }
            }
        } else if ( rowequ ) {
            for (j = 0; j < nrhs; ++j)
                for (i = 0; i < A->nrow; ++i) {
                    Xmat[i + j*ldx] *= R[i];
                }
        }
    } /* end if nrhs > 0 */

    if ( options->ConditionNumber ) {
        /* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
        if ( *rcond < slamch_("E") ) *info = A->ncol + 1;
    }

    if ( nofact ) {
        sQuerySpace(L, U, mem_usage);
        Destroy_CompCol_Permuted(&AC);
    }
    if ( A->Stype == SLU_NR ) {
        Destroy_SuperMatrix_Store(AA);
        SUPERLU_FREE(AA);
    }

}
